Polynomial Operator Equations in Abstract Spaces and Applications: In Abstract Spaces and Applications

ISBN-13: 9780849387029 / Angielski / Twarda / 1998 / 592 str.

Ioannis Argyros; Aoannis K. Argyros

Opis

Polynomial operators are a natural generalization of linear operators. This work presents results about polynomial equations as well as analyzes iterative methods for their numerical solution in various general space settings.

Recenzje

"This book provides a valuable service to those mathematicians working in the area of polynomial operator equations...The theoretical material addressed has a spectrum of applications...applications [that are] quite relevant and important...Anyone doing research in this area should have a copy of this monograph."
Patrick J. Van Fleet, Mathematical and Information Sciences, Huntsville, Texas
"A comprehensive presentation of this rapidly growing field...benefiting not only those working in the field but also those interested in, and in need of, information about specific results or techniques...Clear...Logical...Elegant...The author has achieved the optimum at this point."
- Dr. George Anastassiou, University of Memphis, Tennessee

Spis treści

Introduction
Quadratic Equations and Perturbation Theory
Algebraic Theory of Quadratic Operators
Perturbation Theory
Chandrasekhar's Integral Equation
Anselone and Moore's Equation
Other Perturbation Theorems
More Methods for Solving Quadratic Equations
Banach Algebras
The Majorant Method
Compact Quadratic Equations 83
Finite Rank Equations
Noncontractive Solutions
On a Class of Quadratic Integral Equations with Perturbation
Polynomial Equations in Banach Space
Polynomial Equations
Noncontractive Results
Solving Polynomial Operator Equations in Ordered Banach Spaces
Integral and Differential Equations
Equations of Hammerstein Type
Radiative Transfer Equations
Differential Equations
Integrals on a Separable Hilbert Space
Approximation of Solutions of Some Quadratic Integral Equations in Transport Theory
Multipower Equations
Uniformly Contractive Systems and Quadratic Equations in Banach Space
Polynomial Operators in Linear Spaces
A Weierstrass Theorem
Matrix Representations
Lagrange and Hermite Interpolation
Bounds of Polynomial Equations
Representations of Multilinear and Polynomial Operators on Vector Spaces
Completely Continuous and Related Multilinear Operators
General Methods for Solving Nonlinear Equations
Accessibility of Solutions of Equations by Newton-Like Methods and Applications
The Super-Halley Method
Convergence Rates for Inexact Newton-Like Methods at Singular Points
A Newton-Mysovskii-Type Theorem with Applications to Inexact Newton-Like Methods and Their Discretizations
Convergence Domains for Some Iterative Processes in Banach Spaces Using Outer and Generalized Inverses
Convergence of Inexact Newton Methods on Banach Spaces with a Convergence Structure
References
Glossary of Symbols
Subject Index

O autorze

Argyros\, Ioannis K.